For a family F, let D(F) stand for the family of all sets that can be expressed as F∖G, where F,G∈F. A family F is intersecting if any two sets from the family have non-empty intersection. In this paper, we study the following question: what is the maximum of |D(F)| for an intersecting family of k-element sets? Frankl conjectured that the maximum is attained when F is the family of all sets containing a fixed element. We show that this holds if n⩾50klnk and k⩾50. At the same time, we provide a counterexample for n<4k.